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# Bayes likes Mayor Pete

Summary:
Who has the best chance of beating Donald Trump? A clue can be found using Bayes Theorem. Here is the logic. Let A be the event that a candidate wins the general election, and B be the event that a candidate wins his or her party's nomination. Predictit gives us the betting market's view of P(A) and P(B). It is a safe assumption that P(B / A) = 1, that is, a candidate can win only if nominated. We can then use Bayes theorem to compute P(A / B), the probability that the candidate will win the general election conditional on being nominated. So here are the results for P(A / B) as of now: Buttigieg 0.80Biden 0.77O'Rourke 0.67Sanders 0.65Booker 0.60Yang 0.60Harris 0.57Warren 0.44That is, the betting markets suggest that Mayor Pete would be the strongest candidate if nominated, with

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Who has the best chance of beating Donald Trump? A clue can be found using Bayes Theorem.

Here is the logic. Let A be the event that a candidate wins the general election, and B be the event that a candidate wins his or her party's nomination. gives us the betting market's view of P(A) and P(B). It is a safe assumption that P(B / A) = 1, that is, a candidate can win only if nominated. We can then use Bayes theorem to compute P(A / B), the probability that the candidate will win the general election conditional on being nominated.

So here are the results for P(A / B) as of now:

Buttigieg 0.80
Biden 0.77
O'Rourke 0.67
Sanders 0.65
Booker 0.60
Yang 0.60
Harris 0.57
Warren 0.44

That is, the betting markets suggest that Mayor Pete would be the strongest candidate if nominated, with Joe Biden close behind. (Of course, these numbers will bounce around as the prices in betting markets change.)

By the way, when I did a similar calculation in 2006, Bayes liked Barack Obama.
I am the Robert M. Beren Professor of Economics at Harvard University, where I teach introductory economics (ec 10). I use this blog to keep in touch with my current and former students. Teachers and students at other schools, as well as others interested in economic issues, are welcome to use this resource.